What is tree and spanning tree?
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In this regard, what is Spanning Tree with example?
Given a graph G=(V,E), a subgraph of G that is connects all of the vertices and is a tree is called a spanning tree . For example, suppose we start with this graph: We can remove edges until we are left with a tree: the result is a spanning tree. Clearly, a spanning tree will have |V|-1 edges, like any other tree.
Secondly, what is maximum spanning tree? A maximum spanning tree is a spanning tree of a weighted graph having maximum weight. It can be computed by negating the weights for each edge and applying Kruskal's algorithm (Pemmaraju and Skiena, 2003, p. 336). A maximum spanning tree can be found in the Wolfram Language using the command FindSpanningTree[g].
In this manner, what is meant by spanning tree?
A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges. By this definition, we can draw a conclusion that every connected and undirected Graph G has at least one spanning tree.
What are spanning trees used for?
Real Life Applications Minimum spanning trees are used for network designs (i.e. telephone or cable networks). They are also used to find approximate solutions for complex mathematical problems like the Traveling Salesman Problem. Other, diverse applications include: Cluster Analysis.